1. **State the problem:** Differentiate the function $f(x) = \frac{pn3x}{x}$ with respect to $x$. 2. **Simplify the function:** Since $f(x) = \frac{pn3x}{x}$, we can simplify by canceling $x$ in numerator and denominator: $$f(x) = \frac{pn3\cancel{x}}{\cancel{x}} = pn3$$ 3. **Interpret the simplified function:** The function simplifies to a constant $pn3$ (assuming $pn3$ is a constant coefficient). 4. **Differentiate the constant:** The derivative of a constant with respect to $x$ is zero: $$f'(x) = 0$$ **Final answer:** $$\boxed{0}$$